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Find the Critical Value or Values Of χ2\chi ^ { 2 }

question 18

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Find the critical value or values of χ2\chi ^ { 2 } based on the given information.
-For large numbers of degrees of freedom, the critical χ2\chi ^ { 2 } values can be approximated as follows:
χ2=12(z+2k1) 2\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 } where kk is the number of degrees of freedom and zz is the critical value. To find the lower critical value, the negative zz -value is used, to find the upper critical value, the positive zz -value is used. Use this approximation to estimate the critical value of χ2\chi ^ { 2 } in a two-tailed hypothesis test with n=104\mathrm { n } = 104 and α=0.10\alpha = 0.10 .

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